$$\frac{-4h^2+18h+17}{h-5} = 0$$
Answer
$$ \begin{matrix}h_1 = \dfrac{ 9 }{ 4 }-\dfrac{\sqrt{ 149 }}{ 4 } & h_2 = \dfrac{ 9 }{ 4 }+\dfrac{\sqrt{ 149 }}{ 4 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{-4h^2+18h+17}{h-5} &= 0&& \text{multiply ALL terms by } \color{blue}{ h-5 }. \\[1 em](h-5)\frac{-4h^2+18h+17}{h-5} &= (h-5)\cdot0&& \text{cancel out the denominators} \\[1 em]-4h^2+18h+17 &= 0&& \\[1 em] \end{aligned} $$
$ -4x^{2}+18x+17 = 0 $ is a quadratic equation.
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